Second-harmonic phonon spectroscopy of $\alpha$-quartz

We demonstrate midinfrared second-harmonic generation as a highly sensitive phonon spectroscopy technique that we exemplify using $\alpha$-quartz (SiO$_2$) as a model system. A midinfrared free-electron laser provides direct access to optical phonon resonances ranging from $350\ \mathrm{cm}^{-1}$ to $1400\ \mathrm{cm}^{-1}$. While the extremely wide tunability and high peak fields of an free-electron laser promote nonlinear spectroscopic studies---complemented by simultaneous linear reflectivity measurements---azimuthal scans reveal crystallographic symmetry information of the sample. Additionally, temperature-dependent measurements show how damping rates increase, phonon modes shift spectrally and in certain cases disappear completely when approaching $T_c=846\ \mathrm{K}$ where quartz undergoes a structural phase transition from trigonal $\alpha$-quartz to hexagonal $\beta$-quartz, demonstrating the technique's potential for studies of phase transitions.